3D problems reduce to 2D once you find the right triangle. The skill is spotting it: identify the line and the plane, drop a perpendicular to the plane, and redraw that single right-angled triangle flat before applying Pythagoras or SOHCAHTOA.
Never work inside the 3D picture. Sketch the specific right-angled triangle you need as a separate flat diagram with its lengths labelled.
Drop a perpendicular from the far end of the line to the plane, join the foot to the start point, and the angle sits between the original line and that base line.
You often need Pythagoras first (e.g. a base diagonal) before the trig step that finds the angle.
A cuboid has a base 6 cm by 8 cm and height 5 cm. Find the angle between the space diagonal and the base.
For the same cuboid (6 × 8 × 5), find the length of the space diagonal.
A cuboid measures 3 cm by 4 cm by 12 cm. Calculate the length of its space diagonal.
A cuboid has a square base of side 4 cm and height 10 cm. Find the length of the space diagonal.
A right pyramid has a square base of side 10 cm and vertical height 12 cm. Find the angle between a slant edge and the base.
A cube has side 6 cm. Calculate the angle between a space diagonal and the base of the cube.
A right pyramid has a square base of side 8 cm and vertical height 10 cm. Find the angle between a triangular face and the base.